Transforming Equations into Systems

Thread starter hbomb
Start date Nov 7, 2006
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System System of equations

In summary, a system of equations is a set of two or more related equations that must be solved together to find the values of variables. There are various methods for solving a system of equations, such as substitution, elimination, and graphing. A consistent system has at least one solution, while an inconsistent system has no solution. A system of equations can have more than one solution, known as an infinite solution. It is commonly used in real-life situations to model and solve complex problems in fields such as mathematics, physics, and engineering.

Nov 7, 2006

hbomb

Could someone give a brief run down of how to transform a given equation into a system of first order equations. Example: u"+.5u'+2u=0

How do you transform a given system of equations into a single equation of second order. Example: x1'=3x1-2x2 , x2'=2x1-2x2

Thanks a bunch, because my book doesn't show clearly how to do this.

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Nov 9, 2006

arildno

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Set x=u', for example.

Related to Transforming Equations into Systems

1. What is a system of equations?

A system of equations is a set of two or more equations that are related and must be solved together to find the values of the variables. It is often used to model real-world situations in fields such as mathematics, physics, and engineering.

2. How do you solve a system of equations?

There are several methods for solving a system of equations, including substitution, elimination, and graphing. The best method to use depends on the specific equations and variables involved. It is important to follow the same steps for each equation in the system in order to find a consistent solution.

3. What is the difference between a consistent and an inconsistent system of equations?

A consistent system of equations has at least one solution that satisfies all of the equations. This means that the equations intersect at a single point on a graph. An inconsistent system of equations has no solution that satisfies all of the equations. This means that the equations are parallel and do not intersect on a graph.

4. Can a system of equations have more than one solution?

Yes, a system of equations can have more than one solution. This is known as an infinite solution or infinitely many solutions. In this case, the equations represent the same line or plane, and all points on that line or plane are solutions to the system.

5. How can a system of equations be used in real life?

A system of equations can be used to model and solve real-life problems, such as finding the optimal solution in business or engineering, predicting the path of a moving object, or determining the best combination of ingredients in a recipe. It is a powerful tool for analyzing and solving complex problems in various fields.